On the Theory of Functional-Differential Inclusion of Neutral Type

2002 ◽  
Vol 9 (1) ◽  
pp. 33-52
Author(s):  
A. I. Bulgakov ◽  
V. V. Vasilyev
Keyword(s):  
Cauchy Problem ◽  
Differential Inclusion ◽  
Neutral Type ◽  
Functional Differential Inclusion ◽  
Right Hand ◽  
Functional Differential ◽  
Density Principle

Abstract A Cauchy problem for a functional-differential inclusion of neutral type with a nonconvex right-hand side is investigated. Questions of the solvability of such a problem are considered, estimates analogous to the Filippov's estimates are obtained and the density principle is proved.

On the convergence of the method of finite differences applied to the solution of the initial value problem for functional-differential neutral type equations

1981 ◽  
Vol 89 (3-4) ◽  
pp. 259-265
Author(s):  
N. G. Kazakova ◽  
D. D. Bainov
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Finite Differences ◽  
Neutral Type ◽  
Integral Type ◽  
Initial Value ◽  
Natural Class ◽  
Quadrature Formulae ◽  
The Cauchy Problem ◽  
Functional Differential

SynopsisWhen solving practically the neutral type equations the derivatives are replaced by finite differences while the members of integral type are replaced by quadrature formulae. The paper deals with the convergence of a natural class of methods applied to the Cauchy problem for functional-differential neutral type equations. It is not obligatory for the approximated operators to be compact.

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